Work

Li-Yau Inequality and Related Properties on Metric Star Graphs

Year: 2025

Type: article

Abstract: We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph $$\mathcal {G}$$ G given by the heat kernel formula. As consequence, we derive a Harnack estimate and a Liouville property for bounded harmonic functions. The argument exploits an explicit representation formula for the heat kernel on $$\mathcal {G}$$ G .

Source: Potential Analysis

DOI: 10.1007/s11118-025-10192-6

Author: Fabio Camilli

Institution: University of Chieti-Pescara

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", King Abdullah University of Science and Technology, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni